Michele Bartuccelli and Bin Cheng have been awarded an LMS grant of £1.5K for a visit of Professor Paolo Secchi from the University of Brescia (Italy). Professor Paolo Secchi is a very well known mathematician working in the areas of analysis of solutions of PDEs, Mathematical Theory of Fluid Dynamics such as the Navier-Stokes and the Euler equations, Magnetohydrodynamics and singular limits in hyperbolic PDEs. The research to be carried out at Surrey, in collaboration with Bin and Michele, will be focused on the following topic: when some dimensionless parameters in a fluid model approach zero or infinity, can we rigorously justify the limiting/reduced system, and what should be the correct convergence rate? Although extensively studied since the 1980’s, some crucial questions remain largely open; for example in initial-boundary-value problems with characteristic boundary. Professor Secchi and his collaborators have made important recent contributions to this challenging topic, notably in compressible fluid dynamics. Another aspect of this research that will be addressed is in obtaining sharp estimates in the functional inequalities used to analyze the solutions of PDEs. Indeed such estimates are still largely missing from the study of singular limit problems, but play a key role in bridging PDEs analysis to scientific computing due to the following reasoning: convergence to the singular limits at the numerical level should be consistent, to a satisfactory degree, with theoretical predictions.